Question

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Answer 1

$\bigstar \underline{\underline{\sf \bf Given:-}}$

• Velocity of neutron=v
• Head on collision occurs with nucleus of an atom.
• Mass no of atom = ' A'

$\bigstar \underline{\underline{\sf \bf To\ Find:-}}$

• The fraction of total energy retained by neutron.

$\bigstar \underline{\underline{\sf \bf Solution:-}}$

We know :

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❥Momentum=m×v

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Acc to question,

$=> \sf Momentum\ before\ collision=u(m_1 -m_2)\\\\=>\sf Momentum \ after\ collision=v(m_1+m_2)$

Also,

Initial momentum = final momentum

$:\implies \sf u(m_1-m_2)=v(m_1+m_1)\\\\:\implies \sf \frac{m_1-m_2}{m_1+m_2} =\frac{v}{u}$

$:\implies \sf \frac{v}{u} =\frac{1-A}{1+A} \ ....(1)$

Now ,

We know :

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❥ KE= 1/2(mass)(velocity)²

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Fraction of KE retained is :-

$:\implies \sf \frac{1/2(m)v^2}{1/2(m)u^2} =\frac{v^2}{u^2} \\\\\\\ \ [From\ (1)]\\\\:\implies \sf \frac{v^2}{u^2}=(\frac{1-A}{1+A} )^2\\\\:\implies \boxed{\boxed{\sf (\frac{A-1}{A+1} )^2}}$

Hence, Option(A) is correct.

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HOPE IT HELPS !

Answer 2

Answer:

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